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arXiv · 1701.04541

Fox-Neuwirth-Fuks cells, quantum shuffle algebras, and Malle's conjecture for function fields

Jordan S. Ellenberg·TriThang Tran·Craig Westerland
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Abstract

The purpose of this paper is to prove the upper bound in Malle's conjecture on the distribution of finite extensions of $\mathbb{F}_q(t)$ with specified Galois group. As in previous work of Ellenberg-Venkatesh-Westerland, our result is based upon computations of the homology of braid groups with certain (exponential) coefficients. However, the approach in this paper is new, relying on a connection between the cohomology of Hurwitz spaces and the cohomology of quantum shuffle algebras.

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Jordan S. Ellenberg, TriThang Tran, Craig Westerland. 2017-01-17. Fox-Neuwirth-Fuks cells, quantum shuffle algebras, and Malle's conjecture for function fields. https://arxiv.org/abs/1701.04541

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